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3 years ago

g What is the final velocity of a hoop that rolls without slipping down a 6.92 m high hill, starting from rest

Physics

1 answer:

liberstina [14]3 years ago

5 0

Answer:

The value is $v = 8.24 \ m/s$

Explanation:

From the question we are told that

The height of the hill is $h = 6.92 \ m$

Generally from the law of energy conservation we have that

$PE = KE + RKE$

Here PE is the potential energy of the hoop which is mathematically represented as

$PE = mgh$

KE is the kinetic energy of the hoop which is mathematically represented as

$KE = \frac{1}{2} * m * v^2$

And

RKE is the rotational kinetic energy which is mathematically represented as

$RKE = \frac{1}{2} * I * w^2$

Here I is the moment of inertia of the hoop which is mathematically represented as

$I = m * r^2$

and w is the angular velocity which is mathematically represented as

$w = \frac{v}{r}$

$RKE = \frac{1}{2} * m r^2 * \frac{v}{r} ^2$

=> $RKE = \frac{1}{2} * m r * v^2$

$mgh = \frac{1}{2} * m * v^2 + \frac{1}{2} * m r * v^2$

=> $v = \sqrt{gh}$

=> $v = \sqrt{9.8 * 6.92 }$

=> $v = 8.24 \ m/s$

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One of two 25-year-old identical twins begins a trip on a spaceship traveling at 0.8 c while her twin remains on Earth. The twin

borishaifa [10]

Answer:

This equation is based on twin paradox - a phenomena where one of the twin travels to space at a speed close to speed of light and the other remains on earth. the twin from the space on return discovers that the one on earth age faster.

Solution:

$t_{o}$ = 10 years

v = 0.8c

c = speed of light in vacuum

The problem can be solved by time dilation equation:

$t = \frac{t_{o}}{\sqrt{1 - \frac{v^{2}}{c^{2}}}}$ (1)

where,

t = time observed from a different inertial frame

Now, using eqn (1), we get:

$t = \frac{10}{\sqrt{1 - \frac{(0.8c)^{2}}{c^{2}}}}$

t = 16.67 years

The age of the twin on spaceship according to the one on earth = 25+16.67 =41.66 years

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3 years ago

Why is conserving energy resources not a simple problem with a simple solution?

anyanavicka [17]

Answer:

Because the uncontrolled and unreasonable use of energy resources in the past few decades has led to the depletion of conventional type of resources. Although, measures are taken at the government levels to control the energy consumption, these attempts only meet with little success. Public awareness is the only way to successfully deal with this problem.

Explanation:

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3 years ago

Read 2 more answers

A 2:2 kg toy train is con ned to roll along a straight, frictionless track parallel to the x-axis. The train starts at the origi

Liula [17]

Answer:

a) 10.51 J

b) 3.48 m/s

Explanation:

Given data :

mass of train ( M ) = 2.2 kg

Given initial velocity ( u ) = 1.6 m/s

a) calculating work done by the force over the journey of the train

F = mx + b ------ ( 1 )

m = slope = ( Δ f / Δ x ) = 2.8 / -7.5 = - 0.373 N/m

x = distance travelled on the x axis by the train = 7.5 m

F = force experienced by the train = 2.8 N

x = 0

∴ b = 2.8

hence equation 1 can be written as

F = ( -0.373) x + 2.8 ----- ( 2 )

hence to determine the work done by the force

W = $\int\limits^7_0 { ( -0.373) x + 2.8 )} \, dx$ Note: the limits are actually 7.5 and 0

∴ W ( work done ) = -10.49 + 21 = 10.51 J

b) calculate the speed of the train at the end of its journey

we will apply the work energy theorem

W = 1/2 m*v^2 - 1/2 m*u^2

∴ V^2 = 2 / M ( W + 1/2 M*u^2 ) ( input values into equation )

V^2 = 12.11

hence V = 3.48 m/s

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3 years ago

Three collinear forces,F1=45N west,F2=63N east and an unknown force F3 are applied to an object.The resultant force of the three

Greeley [361]

Take east to be the positive direction. Then the resultant force from adding F₁ and F₂ is

F₁ + F₂ = (-45 N) + 63 N = 18 N

which is positive, so it's directed east.

To this we add a third force F₃ such that the resultant is 12 N pointing west, making it negative, so that

18 N + F₃ = -12 N

F₃ = -30 N

So F₃ has a magnitude of 30 N and points west.

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3 years ago

Distinguish

yaroslaw [1]

Answer:

Velocity and speed both are continuously increasing.

Acceleration is constant.

Explanation:

Speed is defined as length of path covered by a body per unit time. Speed is a scalar quantity that consist of magnitude only and not direction.

Velocity is defined as the displacement per unit times. Displacement is the shortest distance between the two points. It is a vector quantity and hence has a direction in the direction of displacement along with its own magnitude.

Both velocity and speed have same unit of measure which is meter per second in S.I. During free fall in the absence of any air resistance the velocity and speed both will be having a vertical downward direction with continuously increasing magnitude. Tough we are not concerned about the direction when discussing about speed but here both are equal since the motion is linear.

Acceleration is the rate of change in velocity of a body which is a vector quantity. For speed we are concerned about instantaneous acceleration since for a short period of time it may have a specific direction.

During free fall the acceleration is of a body is equal to the acceleration due to gravity and constant when the height of fall is much lesser than the radius of the earth.

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